A162885 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.

1, 45, 1980, 86130, 3746160, 162915390, 7084967670, 308115104220, 13399485132330, 582724430755830, 25341851494598760, 1102080851855063190, 47927918932540448670, 2084316599215116583020, 90643945794494362584930

Offset

0,2

Comments

The initial terms coincide with those of A170764, although the two sequences are eventually different.

Computed with MAGMA using commands similar to those used to compute A154638.

Links

G. C. Greubel, Table of n, a(n) for n = 0..609

Index entries for linear recurrences with constant coefficients, signature (43, 43, -946).

Formula

G.f.: (t^3 + 2*t^2 + 2*t + 1)/(946*t^3 - 43*t^2 - 43*t + 1).

a(n) = 43*a(n-1) + 43*a(n-2) - 946*a(n-3), n > 0. - Muniru A Asiru, Oct 24 2018

G.f.: (1+x)*(1-x^3)/(1 - 44*x + 990*x^3 - 946*x^4). - G. C. Greubel, Apr 28 2019

Maple

seq(coeff(series((x^3+2*x^2+2*x+1)/(946*x^3-43*x^2-43*x+1), x, n+1), x, n), n = 0 .. 20); # Muniru A Asiru, Oct 24 2018

Mathematica

CoefficientList[Series[(t^3+2*t^2+2*t+1)/(946*t^3-43*t^2-43*t+1), {t, 0, 20}], t] (* G. C. Greubel, Oct 24 2018 *)
coxG[{3, 946, -43}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 28 2019 *)

Prog

(PARI) my(t='t+O('t^20)); Vec((t^3+2*t^2+2*t+1)/(946*t^3-43*t^2-43*t+1)) \\ G. C. Greubel, Oct 24 2018
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!(( t^3+ 2*t^2+2*t+1)/(946*t^3-43*t^2-43*t+1))); // G. C. Greubel, Oct 24 2018
(GAP) a:=[45, 1980, 86130];; for n in [4..20] do a[n]:=43*a[n-1]+43*a[n-2] -946*a[n-3]; od; Concatenation([1], a); # Muniru A Asiru, Oct 24 2018
(Sage) ((1+x)*(1-x^3)/(1-44*x+990*x^3-946*x^4)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 28 2019

Crossrefs

Sequence in context: A328351 A203828 A318221 * A163231 A163749 A164330

Adjacent sequences: A162882 A162883 A162884 * A162886 A162887 A162888

Keyword

nonn

Author

John Cannon and N. J. A. Sloane, Dec 03 2009

Status

approved